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This question already has an answer here:

Originally he was seen as a Lieutenant (2 full pips) but later he doesn't have any is referred to as an NCO with the rank of Chief Petty Officer (TNG s4 and DS9)

So it wasn't because of his transfer because s4 of TNG already refers to him as Chief Petty Officer.

marked as duplicate by NKCampbell, Dave Johnson, Edlothiad, Möoz, Blackwood May 4 '17 at 21:47

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The rank of Miles O'Brien was not consistent during his appearance on the shows.

From Wikipedia:

During the story progression of TNG and DS9, O'Brien wears black silver-rimmed insignia, or lieutenant junior grade (TNG: "Encounter at Farpoint"), lieutenant insignia ("Redemption, Part II", "Data's Day", etc.), and then black gold-rimmed insignia (DS9: "Emissary"). Sergey Rozhenko calls him a Chief Petty Officer in "Family" (TNG) but he had been referred to in previous episodes as Lieutenant. Eventually, O'Brien receives a distinct senior chief petty officer's insignia and his rank is emphatically identified in "Hippocratic Oath" (DS9).

From Memory Alpha:

The character of Miles O'Brien, and the exact rank he held in Star Trek, has a history of its own spanning the length of the character's existence.

In thirteen years of the character's appearances, only in the last four was his rank established to be presumably senior chief petty officer (although this term was never directly used on screen). Through various other stages of the character's development, O'Brien was referred to as a crewman, a lieutenant, and various script notes indicated he was a "warrant officer." The novelization of "Emissary" indicated O'Brien held a rank known as "ensign junior grade".

The site then provides a detailed account of the ranks he held on the episodes he appeared; due to its lenght, I've not reported it here, and I encourage you to simply read it at the source.

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